Ouch

Steve McIntyre has followed up on Willis Eschenbach’s simple replication of global climate models. Steve also replicated Giss from forcings using the same simple equations. The result demonstrates that the models are simple linear combinations of assumed forcings. The heart of a top global warming model is exposed in these posts. Ocean currents, hadley cells, cloud formation, aerosols, all pre-assumed linear factors. This is proof that there is no magical attachment to complex physics which would cause models to EVER give unexpected results. Instead, it is a clear demonstration that the opposite problem exists, the result was written before the conclusion.

37 Responses to “Ouch”

“The result demonstrates that the models are simple linear combinations of assumed forcings. The heart of a top global warming model is exposed in these posts. Ocean currents, hadley cells, cloud formation, aerosols, all pre-assumed linear factors.”
Jeff, that’s just completely wrong. It may well be that the global temperature result of model outputs can be emulated by a simpler model. But that doesn’t tell you anything about what a GCM is, and it’s certainly nothing like what you say.

Von Neumann said“With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”
It’s still an emulation, not an elephant.

I’m wrong a lot, but I disagree with you. If there were powerful second order effects, the linear fit to forcings would fail. There would be some match but to see the match be so perfect with no deviations from the complex models does give us a key to their core function.

The fits show that the predictive ability of the models is based on assumptions parameterized to the point that the output is a summation of the inputs. No chance for an unexpected convective instability to cool the planet etc. Just a lousy sum.

Were it a high order equation I would agree. I’ve fit lots of equations in my time, to see one this simple fit so well IS explanatory.

Brian Hsaid

Jeff, well, I disagree too. It’s not an issue of second order effect – the GCM could well deviate even with everything still linear. The fact that the temperature tracks forcings moderately well just reflects that heat is conserved with no great delays on the timescale, even though the flow patterns as solved by the GCM are complex.

GCM’s do a great deal more than just predict global mean surface temperature.

But why I called what you said completely wrong is that it says “the models are simple linear combinations …” etc. And they just aren’t. They are numerical Navier-Stokes solvers.

“But why I called what you said completely wrong is that it says “the models are simple linear combinations …” etc. And they just aren’t. They are numerical Navier-Stokes solvers.”

If the Navier Stokes solver doesn’t affect the outcome of the energy balance, what is the purpose of projecting global temperature with it? The solver in the hadley cell example of CAM3 sure looked pretty weak to me? :D

John F. Pittmansaid

JeffID, you need to read more carefully. The information posted by Willis and SteveMcI is a linear approximation of the GCM’s output. The results do not demonstrate that the models are simple linear combinations (or approximations as some pointout)of assumed forcings, but that the output on a short time period can be emulated quite well by such a linearization. This is not unknown. This highlights why Dr Kreiss, Browning, and Gravel’s works on the exponential growth of error in systems that are lineariztions (ODE’s) rather than the true underlying reality of PDE’s.

I don’t agree with your interpretation that a linear approximation of GCM output should match that well. To me it is quite telling about the content of the GCM itself. It means that non-linear effects so strongly advertized – i.e. Navier Stokes solutions or it’s just the math commentary from RC fare, have been parameterized right out of the models. Where is the feedback from the hadley cell to increased warming? If it is there, it appears linear or very weak in GISS climate models.

I really do need to spend some time explaining that to people more. When you see a linear approximation fit so well, the second, third, fourth order effects must be minimal right? Just why wouldn’t the earth convect faster with increased forcing?

Sorry for the spelling, I am too busy to be blogging but I don’t agree with the commentary that this is a not an indication of the nature of the models.

John F. Pittmansaid

JeffID I did not disagree with you except to point out that it is worse than you think. But rather, that the match and the expected increase in error means either that the Most Probable Causes’s are that the models are overtuned guarenteeing to be incorrect when used past about 30 years, or such “tricks” as hyperviscosity have been used to the point that the result is a linearization of GISS forcings, and little more.

Jeremysaid

Nick Stokes said
May 17, 2011 at 7:48 am
…But why I called what you said completely wrong is that it says “the models are simple linear combinations …” etc. And they just aren’t. They are numerical Navier-Stokes solvers.

I agree that Jeff probably isn’t correct in saying that the GCM’s are linear. I also agree with Jeff that the probability that a linear combination of forcings matches so well with the GCM result is disturbing to say the least.

I’ve never heard of Navier-stokes equations until you mentioned them. It was interesting to read that Wikipedia states that there is no proof of the existence of a three-dimensional solution to navier-stokes equations. Mind you, this doesn’t mean there isn’t one, but it does mean that if wikipedia is accurate in this case (and it is usually reliable on questions of math/physics), the GCM modelers are using unproven math if they are truly trying to solve for earth’s atmosphere using that method. I found that humorous.

RBsaid

But there is another fundamental, often implicit, assumption that underlies nearly all such discussions: the simplicity of the forced response. Without this simplicity, there is little point in using concepts like “forcing” or “feedback” to help us get our minds around the problem, or in trying to find simple observational constraints on the future climatic response to increasing CO2. The simplicity I am referring to here is “emergent”, roughly analogous to that of a macroscopic equation of state that emerges, in the thermodynamic limit, from exceedingly complex molecular dynamics.

RB – an excellent link. I do find it interesting to read the claim that the amazingly complex model ‘should’ break down to a simple formula. How do we really know when individual sections such as hadley cells are reduced to simple assumptions rather than complex phenomena within the models? Surely the modelers must realize that their own simplifications are part of the bulk result.

Jeremy #11,
The GCM modellers aren’t using unproven math. It’s true that there is no existence proof – ie that you can be certain of a solution for prescribed initial conditions. But in practice CFD methods do yield numerical solutions, and once you have one, you can verify that it does satisfy the equations.

And if you’re worried about GCM’s and unproven math – well, commercial aircraft are designed using the same “unproven” math.

Jeff Idsaid

“And if you’re worried about GCM’s and unproven math – well, commercial aircraft are designed using the same “unproven” math.”

No way Nic, I do owe you one. The NS equations are not the problems in GCM’s and calling a GCM a NS solver is a stretch by itself. Yes it is a component but don’t claim that GCM’s are the same math here and expect not to get noticed.

Jeremysaid

For the Aerospace industry, verifying that you have a valid solution to a fluid problem involves building a physical model and sticking it in a wind tunnel. Wind tunnels existed before computer models in this case, so validating methodology there seems a reasonable possibility.

curioussaid

Nick – please can you give some examples or insights into what GCMs do well? This isn’t snark – I’d value your insights. To be up front, the view I’ve formed, following at a distance, is that they are nigh on useless. Willis and SteveMc’s posts have reinforced this view. On the CA thread Mosher has made comments that they (GCMs) are doing lots by solving in three d boxes and that the oft quoted Global Avg Temp metric output disguises a lot of the complexity that lies beneath. I can accept that may be the case and I’d draw an analogy with stress checking in FEA – a simple force over area calc can give you the average stress on parallel loaded faces but, in a complex geometry part, what happens to stress levels as the load is transferred from one face to another is another matter. Solving consistently and repeatably with results that tie in to observations gives confidence that the FEA is valid. Do you have any examples of this type (or otherwise) which would support the output of GCMs as having some value? Or if my naive view is wrong please set me straight. Thanks.

Jeff Idsaid

Your experience with FEA is close to my own. The ‘stress field’ analog is so arbitrarily gridded that no effort is made to examine. In fact, some of the highest response potential energy flow probabilities are linearized and defined well outside of the NS equations. They are completely (or nearly) moot regarding energy transfer in multiple aspects of Climate Models. That’s why Nick really needs to back away from his last statement.

Real blogging is tough, everyone gets to be wrong sometimes.

If you read the gridding methods of a GCM, you might quit climate models entirely.

Curious #18,
GCM’s operate (famously) in a difficult world for testing. They predict the future on a multi-decadal scale, and they are really all we have for doing that. But we aren’t there yet. And they tell us a lot about the current air/ocean system. But the atmosphere is well observed, so all that really shows up there are the discrepancies.

They are an outgrowth of numerical weather prediction. Though some people scoff at that, I think it has been hugely successful. Where I am you can get an eight day detailed forecast of rainfall. It isn’t infallible, but in my experience is very good. This is the same technology, and it isn’t just a linear combination of a few inputs.

As I said, the purpose of GCM’s is to predict the medium and long term future. Time will tell. As to how they do at things we can test, here’s a recent multi-author paper involving Hansen, which gives a detailed picture of what modelE can and can’t do. The deficiencies are in 2.4. They are significant, but the rest of the long paper is about what it can do, and it is a lot.

Now telling us what we already knew about the present isn’t so valuable, and that is why there is so much focus on what they do less well. But a program like Willis’, essentially curve fitting, can do well with one variable currently observed, but makes no real basis for prediction. A GCM which makes a physically based calculation can reasonably be expected to do as well in the future as it did to date. The physics it usues won’t change.

Re: Jeremy (May 17 18:49),
You don’t need a wind tunnel to check that a computed solution actually satisfies the equations, which is what the existence theorem demonstrates. A wind tunnel would check whether the equations actually apply.

But aerospace is using them less and less. Even in the 90’s, the Boeing 777 was designed with CFD. As Wiki says:“Boeing was initially not convinced of CATIA’s abilities and built a physical mock-up of the nose section to verify its results. The test was so successful that additional mock-ups were canceled.[34]”

Jeff Idsaid

Finite difference/volume/pressure level are all simply different gridding methods. While I agree they are appropriate guesses, they are not homogeneously used to represent the segmentation of all aspects of the CAM GCM. While plenty complex, it simply isn’t as complete a model as your work represented. Estimations and sub-gridded or forced grid approximations exist right in the middle of otherwise cleaner math.

Ugly kludge, is the best phrase for it and GCM’s don’t deserve to be compared to aerodynamic solutions because of that. Lack of verification, over assumption and controlled unknowns are prevalent. BTW, I believe you are aware of these facts.

Just to be clear Nick. There is a mathematical completeness to your own flow diagrams which is simply unachievable in GCM’s. The fact that you would compare a GCM to the completeness of NS solved flow is an oddity to me. I’ve got enough history now to know that you get the difference and your representation of them as the same as NS is equally in error to my poorly qualified statements about linearity.

We know GCM’s aren’t linear, these fits show them to be more linear than not. We also know that assumptions consume GCM’s and pollute the basic flow equtns.

I find the overwhelming linearity very much disconcerting but not unsurprising given the assumptions in the major feedback parametrizations. Don’t forget Cam3 hadley cells are laid out on a fixed grid rather than NS defined flow.

Mark Tsaid

If you really want to get into linearity try to grasp the Hansen version of feedback – mathematically… got a problem if you use that AND think Willis’ result is “expected,” hehe. Gaurantee the guys writing the code don’t have the background to grasp what they’re doing, certainly the climatologists don’t.

Jeff,
You can get a CFD program to model fast liquid flow in a pipe. You’ll need to if you want to know about erosion, scaling, heat exchange etc.

And you can get a simple model which will predict mass outflow, as the CFD program will. Basically, it equals inflow. That doesn’t mean that the CFD program is just doing simple accounting.

All CFD-style programs have to deal with sub-grid scale modelling. In wind tunnel models etc, the issue is turbulence. In the atmosphere, there are many such issues. Updrafts, aerosols, clouds. Getting the model physics right is an issue. But it isn’t generally grid-related, and doesn’t diminish the mathematics.

There is a grid issue at the bottom boundary. This is analogous to the problem of turbulence modelling near walls – generally solved with wall functions. The air-ocean interface is an issue. But it’s a physics issue mainly, rather than numerical. Once the cross-boundary fluxes are known, transport in the atmosphere is solved just as with turbulence.

Jeff Idsaid

How is Hadley cell distribution determined in CAM3 by math with flexibility or math with rigidity?

The ability for the models to flex is overstated and the result is a nearly perfect linear response to forcings. This is likely completely unnatural. That is my point above, and if we live for another 20 years, I think my point will be born out.

Gridding is quite coarse in the climate models, far too coarse to properly model convection. It is therefore estimated in bulk. Cloud cover is modeled the same ways. Not by NS or pressure but by parametrized generalizations. You can’t call it as good as a pipe flow model where the flow is actually determined from math, shear, viscosity etc. You also can’t test any sub-level estimates against experiment to determine accuracy. I’m quite surprised that you, of all people, would place any faith in the climate model estimates. What happens to heat transfer in your pipe flow when your Raleigh number is estimated wrong? You do an experiment and change the number. In climate modeling, the numbers which need estimation are difficult to come by. Aerosols, cosmic ray, TSI, ocean flow, atmospheric cloud formation, convection, hadley cell strength, on and on….

They are guessed, inserted and lo and behold, the whole thing comes down to a linear response to a few assumed forcings. Despite what you say, this is telling about the assumptions in GCM’s.

TimTheToolMansaid

“They are guessed, inserted and lo and behold, the whole thing comes down to a few forgings with a linear response to a few assumed forcings. Despite what you say, this is telling about the assumptions in GCM’s.”

With the new findings on cosmic ray forcings on cloud creation, I can imagine how the AGWers will recreate the earth’s cosmic ray “history” to make their models fit ever better with the past climate. Its going to be another tweakable knob they’ll have and who’s to argue with whatever values they choose?

Jeremysaid

You don’t need a wind tunnel to check that a computed solution actually satisfies the equations…

I understand that wind tunnels are falling out of favor with the rise of simulation. I’m simply saying that the use of this math in it’s application to building airplanes grew out of already established understanding of how the system worked. The use of computer models here grew and developed alongside easy access to experimental methods of validation.

I am not trying to pin you down when I repeat the question, What does climate science use to validate their use in GCMs if their isn’t an existence proof/theorem for a 3D navier-stokes? This is genuine curiosity here, so if my question is poorly posed, please help me out.

DeWitt Paynesaid

CFD still isn’t all there. One Formula 1 team decided that they could design their car using CFD without wind tunnel tests. It’s slow and the person in charge has left the company. Even wind tunnels aren’t perfect. Ferrari, for one, has had problems with calibrating wind tunnel results to on track results. Airplanes are easy by comparison.

Jeremy #30,
Even quadratic equations aren’t guaranteed to have (real) solutions. But there’s a solving process, and if you use it and find something that you think is a solution, you can substitute it in the equation to check. And indeed, in that case the solving process can fail.

With Navier-Stokes, the lack of an existence proof is not a practical problem. There’s a solution process, and in practice it can be made to yield an answer which satisfies the discretised equations to numerical accuracy. That’s all a numerical process can do. The real issue is stability (turbulence). There are well established ways of dealing with that.

That’s what I mean by saying you don’t use a wind tunnel to check that the maths is right. You can do that with the computer. A wind tunnel checks the applicability of the maths.

curioussaid

The eight day rainfall forecast example makes me wonder what was the starting point for this model? Is it an eight day chunk of output from a model spun up from a say 1950 start point in time and run through to say 2050? Something suggests to me it isn’t – I’m in the UK and the bits of longrange model forecasts I cross checked a while ago were not good indicators of what the weather we had. You are asserting that the GCMs are best for medium to long range forecasts so I think eight day forecast success can only support this if the model was started at some medium to long range time in the past? Also how does the model compare to other rainfall forecasting methods? From the coverage over here I have the impression that parts of Aus were caught by surprise by heavy rainfall this year – how did the models do at predicting that? Whether it was good or bad, is there anything to be learnt from it?

Re: FEA/CFD etc – yes the maths in established products is sound and the results are reliable for properly understood and specified problems. I don’t know how this shook out but this story stuck in my mind re: FEA in aerospace:

“Scott Fancher, the head of the Dreamliner program, explained the structural problem in a conference call early Tuesday morning.

He said that late in May engineers, performing wing-bend tests on the airplane that is set aside inside the factory specifically for ground testing, found that strain gauges showed higher stress than predicted by the computer models at multiple points along the upper part of the wing-to-body join.”

Curious #33,
I didn’t follow the Qld predictions but the Victorian predictions of heavy rain were spot on – amounts, regions, including the way the rain carefully avoided flooding our water supply catchments :(

On FEA and the Dreamliner, that of course isn’t CFD. But it seems from the article that the problem was the composite material not meeting specs, not faulty FEA.

curioussaid

34 Nick – good to know that there are some models with predictive power… I’ll not press you on the timescales point… ;-)

Re: Dreamliner – I wasn’t suggesting it was faulty FEA. The point I was making is that one can have sound maths and theory which if misapplied will not give reliable results. The misapplication can be due to incorrect problem specification, inadequate knowledge of materials or other physical conditions, whatever – the end result is the same: dodgy outcome. Dreamliner was costly but when the theory failed the validation they bit the the bullet and investigated to solve the problem. Your nosecone example is just another instance of the same thing – a validation test; only in that case it was one that was passed.

Maybe as Jeff said upthread the day will come when we’ll get real predictive power from GCMs but IMO that is a long way off. If we do then maybe we could/should put some weight on them but right now I think that they are leading toward, at best, inefficient policy.

But I will read the Hansen et al paper and I’ll let you know if it changes my mind … :-)